Finite Group Databasebeta

← #14685163

Subgroups — #14685163

Order 2816.

3654 conjugacy classes of subgroups.

The subgroup lattice has 926 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66931C211yesmaximal, characteristic, complemented
2C23×C22⋊Dic11C211yesmaximal, characteristic
3C2×#10622560C212yesmaximal, complemented
4C2×#10622860C211yesmaximal, characteristic
5#13066861C212yesmaximal, complemented
6#13066859C212yesmaximal, complemented
7#13066859C212yesmaximal, complemented
8#13066838C211yesmaximal, characteristic, complemented
9#13066838C211yesmaximal, characteristic, complemented
10#13066838C211yesmaximal, characteristic, complemented
11C2×C11×#379C211yesmaximal, characteristic
12C26×C11C2211yescharacteristic
13C24×Dic11C2211yescharacteristic
14C24×Dic11C2211yescharacteristic
15C23×Dic22C2211yescharacteristic, complemented
16C22×C11×C22⋊C4C2211yescharacteristic
17C22×C11×C22⋊C4C2212yes—
18C22×C11×C22⋊C4C2212yes—
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C22⋊Dic11—24no—
21C22×C22⋊Dic11—28no—
22C22×C22⋊Dic11C2211yescharacteristic
23C22×C22⋊Dic11C2212yes—
24C22×C22⋊Dic11C2212yes—
25C22×C22⋊Dic11C2212yes—
26C22×C22⋊Dic11C2211yescharacteristic
27C22×C22⋊Dic11C2212yes—
28C22×C4⋊Dic11C2211yescharacteristic, complemented
29C22×Dic11⋊C4C2211yescharacteristic, complemented
30C22×Dic11⋊C4C2211yescharacteristic, complemented
31C2×#66931—24no—
32C2×#66931—24no—
33C2×#66931—24no—
34C11×#379—24no—
35#10622860—24no—
36C2×C11⋊#95C2212yescomplemented
37C2×C11⋊#95C2212yescomplemented
38C2×C11⋊#95C2212yescomplemented
39C2×C11⋊#95C2212yescomplemented
40C2×C11⋊#95C2212yescomplemented
41C2×C11⋊#95C2212yescomplemented
42#10622560—28no—
43C25×C11—24no—
44C25×C11—22no—
45C25×C11—24no—
46C25×C11—22no—
47C25×C11—22no—
48C25×C11—22no—
49C25×C11—22no—
50C25×C11—22no—
51C25×C11—42no—
52C25×C11—42no—
53C25×C11Q814yescomplemented
54C25×C11C2312yes—
55C25×C11C2311yescharacteristic
56C23×C4×C11C2312yes—
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×Dic11—22no—
60C23×Dic11—22no—
61C23×Dic11—22no—
62C23×Dic11—24no—
63C23×Dic11—24no—
64C23×Dic11—22no—
65C23×Dic11—22no—
66C23×Dic11—42no—
67C23×Dic11—42no—
68C23×Dic11D414yes—
69C23×Dic11C2312yes—
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2311yescharacteristic
73C23×Dic11C2312yes—
74C23×Dic11C2311yescharacteristic
75C22×Dic22—22no—
76C22×Dic22—22no—
77C22×Dic22—22no—
78C22×Dic22—24no—
79C22×Dic22—42no—
80C2×C11×C22⋊C4—22no—
81C2×C11×C22⋊C4—22no—
82C2×C11×C22⋊C4—24no—
83C2×C11×C22⋊C4—22no—
84C2×C11×C22⋊C4—24no—
85C2×C11×C22⋊C4—22no—
86C2×C11×C22⋊C4—22no—
87C2×C11×C22⋊C4—24no—
88C2×C11×C22⋊C4—24no—
89C2×C11×C22⋊C4—42no—
90C2×C11×C22⋊C4—42no—
91C2×C11×C22⋊C4D414yes—
92C2×C22⋊Dic11—232no—
93C2×C22⋊Dic11—22no—
94C2×C22⋊Dic11—22no—
95C2×C22⋊Dic11—24no—
96C2×C22⋊Dic11—24no—
97C2×C22⋊Dic11—24no—
98C2×C22⋊Dic11—24no—
99C2×C22⋊Dic11—24no—
100C2×C22⋊Dic11—24no—
101C2×C22⋊Dic11—22no—
102C2×C22⋊Dic11—22no—
103C2×C22⋊Dic11—24no—
104C2×C22⋊Dic11—22no—
105C2×C22⋊Dic11—24no—
106C2×C22⋊Dic11—24no—
107C2×C22⋊Dic11—42no—
108C2×C22⋊Dic11—42no—
109C2×C22⋊Dic11D414yes—
110C2×C22⋊Dic11D418yes—
111C2×C4⋊Dic11—22no—
112C2×C4⋊Dic11—22no—
113C2×C4⋊Dic11—22no—
114C2×Dic11⋊C4—22no—
115C2×Dic11⋊C4—22no—
116C2×Dic11⋊C4—22no—
117C2×Dic11⋊C4—22no—
118C2×Dic11⋊C4—22no—
119C2×Dic11⋊C4—22no—
120#66931—232no—
121C11⋊#95—24no—
122C11⋊#95—24no—
123C11⋊#95—24no—
124C11⋊#95—42no—
125C11⋊#95—42no—
126C11⋊#95—42no—
127#14717—111nomaximal, Sylow
128C24×C11—22no—
129C24×C11—22no—
130C24×C11—22no—
131C24×C11—22no—
132C24×C11—28no—
133C24×C11—28no—
134C24×C11—216no—
135C24×C11—28no—
136C24×C11—216no—
137C24×C11—22no—
138C24×C11—22no—
139C24×C11—22no—
140C24×C11—22no—
141C24×C11—22no—
142C24×C11—22no—
143C24×C11—22no—
144C24×C11—22no—
145C24×C11—22no—
146C24×C11—22no—
147C24×C11—22no—
148C24×C11—22no—
149C24×C11—28no—
150C24×C11—28no—
151C24×C11—48no—
152C24×C11—48no—
153C24×C11—48no—
154C24×C11—48no—
155C24×C11—48no—
156C24×C11—48no—
157C24×C11—48no—
158C24×C11—48no—
159C24×C11—48no—
160C24×C11—44no—
161C24×C11—44no—
162C24×C11—48no—
163C24×C11—44no—
164C24×C11—44no—
165C24×C11—44no—
166C24×C11—44no—
167C24×C11C2×D414yes—
168C24×C11C2×D412yes—
169C24×C11C2×D412yes—
170C24×C11C2×D412yes—
171C24×C11C2×Q814yes—
172C24×C11C2×Q812yes—
173C24×C11#4114yes—
174C24×C11#4112yes—
175C24×C11#4112yes—
176C24×C11#4112yes—
177C24×C11C2411yescharacteristic
178C22×C4×C11—22no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—22no—
184C22×C4×C11—22no—
185C22×C4×C11—22no—
186C22×C4×C11—22no—
187C22×C4×C11—22no—
188C22×C4×C11—22no—
189C22×C4×C11—22no—
190C22×C4×C11—22no—
191C22×C4×C11—22no—
192C22×C4×C11—22no—
193C22×C4×C11C2×D412yes—
194C22×C4×C11C2×D412yes—
195C22×Dic11—28no—
196C22×Dic11—28no—
197C22×Dic11—28no—
198C22×Dic11—21no—
199C22×Dic11—21no—
200C22×Dic11—22no—
201C22×Dic11—21no—
202C22×Dic11—21no—
203C22×Dic11—21no—
204C22×Dic11—21no—
205C22×Dic11—21no—
206C22×Dic11—21no—
207C22×Dic11—22no—
208C22×Dic11—22no—
209C22×Dic11—22no—
210C22×Dic11—22no—
211C22×Dic11—22no—
212C22×Dic11—22no—
213C22×Dic11—22no—
214C22×Dic11—22no—
215C22×Dic11—22no—
216C22×Dic11—22no—
217C22×Dic11—22no—
218C22×Dic11—22no—
219C22×Dic11—22no—
220C22×Dic11—22no—
221C22×Dic11—22no—
222C22×Dic11—22no—
223C22×Dic11—22no—
224C22×Dic11—22no—
225C22×Dic11—22no—
226C22×Dic11—44no—
227C22×Dic11—48no—
228C22×Dic11—48no—
229C22×Dic11—48no—
230C22×Dic11—48no—
231C22×Dic11—44no—
232C22×Dic11—44no—
233C22×Dic11C2×D414yes—
234C22×Dic11C2×D412yes—
235C22×Dic11C2×D412yes—
236C22×Dic11C2×D412yes—
237C22×Dic11C2×D414yes—
238C22×Dic11C2×D412yes—
239C2×Dic22—28no—
240C2×Dic22—48no—
241C2×Dic22—48no—
242C2×Dic22—44no—
243C2×Dic22—44no—
244C11×C22⋊C4—28no—
245C11×C22⋊C4—48no—
246C11×C22⋊C4—48no—
247C11×C22⋊C4—44no—
248C22⋊Dic11—216no—
249C22⋊Dic11—216no—
250C22⋊Dic11—28no—
251C22⋊Dic11—48no—
252C22⋊Dic11—48no—
253C22⋊Dic11—44no—
254C4⋊Dic11—28no—
255Dic11⋊C4—28no—
256Dic11⋊C4—28no—
257C22×C22⋊Q8—111no—
258C23×C22⋊C4—111no—
259C2×#393—112no—
260C2×#379—111no—
261C2×#379D1111yescharacteristic
262#1439—112no—
263#1439—112no—
264#1439—112no—
265C22⋊#95—111no—
266C22⋊#95—111no—
267C22⋊#95—111no—
268C23×C11—22no—
269C23×C11—24no—
270C23×C11—22no—
271C23×C11—24no—
272C23×C11—22no—
273C23×C11—22no—
274C23×C11—24no—
275C23×C11—24no—
276C23×C11—24no—
277C23×C11—24no—
278C23×C11—24no—
279C23×C11—24no—
280C23×C11—24no—
281C23×C11—24no—
282C23×C11—24no—
283C23×C11—24no—
284C23×C11—232no—
285C23×C11—24no—
286C23×C11—24no—
287C23×C11—24no—
288C23×C11—24no—
289C23×C11—24no—
290C23×C11—24no—
291C23×C11—24no—
292C23×C11—24no—
293C23×C11—24no—
294C23×C11—24no—
295C23×C11—24no—
296C23×C11—24no—
297C23×C11—24no—
298C23×C11—24no—
299C23×C11—24no—
300C23×C11—24no—
301C23×C11—24no—
302C23×C11—24no—
303C23×C11—432no—
304C23×C11—432no—
305C23×C11—416no—
306C23×C11—416no—
307C23×C11—416no—
308C23×C11—416no—
309C23×C11—416no—
310C23×C11—432no—
311C23×C11—432no—
312C23×C11—42no—
313C23×C11—42no—
314C23×C11—42no—
315C23×C11—42no—
316C23×C11—42no—
317C23×C11—42no—
318C23×C11—42no—
319C23×C11—42no—
320C23×C11—42no—
321C23×C11—42no—
322C23×C11—42no—
323C23×C11—42no—
324C23×C11—42no—
325C23×C11—42no—
326C23×C11—42no—
327C23×C11—42no—
328C23×C11—416no—
329C23×C11#12014yes—
330C23×C11C22⋊Q814yes—
331C23×C11C22⋊Q814yes—
332C23×C11C22⋊Q814yes—
333C23×C11C22⋊Q818yescomplemented
334C23×C11#12414yes—
335C23×C11#12414yes—
336C23×C11#12414yes—
337C23×C11C22×D411yescharacteristic
338C23×C11C22×D412yes—
339C23×C11C22×D411yescharacteristic
340C23×C11C22×D411yescharacteristic
341C23×C11C22×Q811yescharacteristic
342C23×C11C2×#4111yescharacteristic
343C23×C11C2×#4111yescharacteristic
344C23×C11C2×#4112yes—
345C23×C11C2×#4111yescharacteristic
346C23×C11H(5,𝔽2)12yes—
347C23×C11H(5,𝔽2)12yes—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—24no—
351C2×C4×C11—24no—
352C2×C4×C11—41no—
353C2×C4×C11—41no—
354C2×C4×C11—41no—
355C2×C4×C11—41no—
356C2×C4×C11—42no—
357C2×C4×C11—42no—
358C2×C4×C11—42no—
359C2×C4×C11—42no—
360C2×C4×C11—42no—
361C2×C4×C11—42no—
362C2×C4×C11—42no—
363C2×C4×C11—42no—
364C2×C4×C11—42no—
365C2×Dic11—22no—
366C2×Dic11—22no—
367C2×Dic11—24no—
368C2×Dic11—24no—
369C2×Dic11—22no—
370C2×Dic11—22no—
371C2×Dic11—22no—
372C2×Dic11—22no—
373C2×Dic11—24no—
374C2×Dic11—22no—
375C2×Dic11—24no—
376C2×Dic11—24no—
377C2×Dic11—24no—
378C2×Dic11—24no—
379C2×Dic11—416no—
380C2×Dic11—416no—
381C2×Dic11—41no—
382C2×Dic11—41no—
383C2×Dic11—42no—
384C2×Dic11—41no—
385C2×Dic11—41no—
386C2×Dic11—42no—
387C2×Dic11—42no—
388C2×Dic11—42no—
389C2×Dic11—42no—
390C2×Dic11—42no—
391C2×Dic11—42no—
392C2×Dic11—42no—
393C2×Dic11—42no—
394C2×Dic11—42no—
395C2×Dic11—42no—
396C2×Dic11—42no—
397C2×Dic11—42no—
398C2×Dic11—42no—
399C2×Dic11—42no—
400C2×Dic11#12014yes—
401Dic22—416no—
402C26C2×D1111yescharacteristic
403C23×Q8—111no—
404C24×C4—111no—
405C24×C4—111no—
406C2×C22⋊Q8—224no—
407C2×C22⋊Q8—224no—
408C2×C22⋊Q8—224no—
409C22×C4⋊C4—111no—
410C22×C4⋊C4—111no—
411C22×C4⋊C4—111no—
412C22×C22⋊C4—112no—
413C22×C22⋊C4—111no—
414C22×C22⋊C4—112no—
415C22×C22⋊C4—111no—
416C22×C22⋊C4—112no—
417C22×C22⋊C4—112no—
418C22×C22⋊C4—228no—
419C22×C22⋊C4—224no—
420C22×C22⋊C4C2×D1111yescharacteristic
421C22×C22⋊C4C2×D1112yes—
422C22×C22⋊C4C2×D1112yes—
423C22×C22⋊C4C2×D1111yescharacteristic
424#393—228no—
425#379—24no—
426#379—224no—
427C2×#95—112no—
428C2×#95—112no—
429C2×#95—112no—
430C2×#95—112no—
431C2×#95—112no—
432C2×#95—112no—
433C22×C11—24no—
434C22×C11—24no—
435C22×C11—24no—
436C22×C11—24no—
437C22×C11—24no—
438C22×C11—24no—
439C22×C11—28no—
440C22×C11—28no—
441C22×C11—28no—
442C22×C11—28no—
443C22×C11—28no—
444C22×C11—28no—
445C22×C11—28no—
446C22×C11—464no—
447C22×C11—44no—
448C22×C11—44no—
449C22×C11—44no—
450C22×C11—44no—
451C22×C11—44no—
452C22×C11—44no—
453C22×C11—44no—
454C22×C11—44no—
455C22×C11—44no—
456C22×C11—44no—
457C22×C11—44no—
458C22×C11—44no—
459C22×C11#39318yescomplemented
460C22×C11C2×#12011yescharacteristic
461C22×C11C2×#12011yescharacteristic
462C22×C11C2×C22⋊Q811yescharacteristic
463C22×C11C2×C22⋊Q812yes—
464C22×C11C2×C22⋊Q811yescharacteristic
465C22×C11C2×C22⋊Q811yescharacteristic
466C22×C11#52511yescharacteristic
467C22×C11#52512yes—
468C22×C11C2×#12411yescharacteristic
469C22×C11C2×#12411yescharacteristic
470C22×C11C2×#12411yescharacteristic
471C22×C11#53411yescharacteristic
472C22×C11#53511yescharacteristic
473C22×C11#53812yes—
474C22×C11#54312yes—
475C22×C11D4212yes—
476C22×C11D4212yes—
477C22×C11#54612yes—
478C22×C11#54612yes—
479C22×C11#54612yes—
480C22×C11#54612yes—
481C22×C11#55112yes—
482C22×C11#55112yes—
483C4×C11—42no—
484C4×C11—42no—
485C4×C11—82no—
486Dic11—24no—
487Dic11—42no—
488Dic11—42no—
489Dic11—42no—
490Dic11—44no—
491Dic11—82no—
492C25—24no—
493C25—22no—
494C25—24no—
495C25—22no—
496C25—22no—
497C25—22no—
498C25—22no—
499C25—22no—
500C25—42no—
501C25—42no—
502C25Dic2214yescomplemented
503C25C22×D1112yes—
504C25C22×D1111yescharacteristic
505C22×Q8—222no—
506C22×Q8—222no—
507C22×Q8—224no—
508C22×Q8—222no—
509C22×Q8—442no—
510C23×C4—111no—
511C23×C4—111no—
512C23×C4—111no—
513C23×C4—111no—
514C23×C4—112no—
515C23×C4—114no—
516C23×C4—112no—
517C23×C4—224no—
518C23×C4—224no—
519C23×C4—222no—
520C23×C4—222no—
521C23×C4—222no—
522C23×C4—222no—
523C23×C4—222no—
524C23×C4—442no—
525C23×C4—442no—
526C23×C4C22×D1112yes—
527C23×C4C22×D1111yescharacteristic
528C23×C4C22×D1111yescharacteristic
529C22⋊Q8—2232no—
530C2×C4⋊C4—222no—
531C2×C4⋊C4—222no—
532C2×C4⋊C4—222no—
533C2×C4⋊C4—222no—
534C2×C4⋊C4—222no—
535C2×C4⋊C4—222no—
536C2×C4⋊C4—222no—
537C2×C4⋊C4—222no—
538C2×C4⋊C4—222no—
539C2×C22⋊C4—22no—
540C2×C22⋊C4—22no—
541C2×C22⋊C4—24no—
542C2×C22⋊C4—24no—
543C2×C22⋊C4—22no—
544C2×C22⋊C4—22no—
545C2×C22⋊C4—22no—
546C2×C22⋊C4—24no—
547C2×C22⋊C4—24no—
548C2×C22⋊C4—42no—
549C2×C22⋊C4—42no—
550C2×C22⋊C4—118no—
551C2×C22⋊C4—114no—
552C2×C22⋊C4—224no—
553C2×C22⋊C4—224no—
554C2×C22⋊C4—224no—
555C2×C22⋊C4—224no—
556C2×C22⋊C4—2232no—
557C2×C22⋊C4—224no—
558C2×C22⋊C4—222no—
559C2×C22⋊C4—222no—
560C2×C22⋊C4—224no—
561C2×C22⋊C4—224no—
562C2×C22⋊C4—222no—
563C2×C22⋊C4—222no—
564C2×C22⋊C4—224no—
565C2×C22⋊C4—224no—
566C2×C22⋊C4—222no—
567C2×C22⋊C4—442no—
568C2×C22⋊C4—442no—
569C2×C22⋊C4C22⋊D1114yes—
570#95—224no—
571#95—224no—
572#95—224no—
573#95—442no—
574#95—442no—
575#95—442no—
576C2×C11—28no—
577C2×C11—48no—
578C2×C11C2×#39311yescharacteristic
579C2×C11#240311yescharacteristic
580C2×C11#240411yescharacteristic
581C2×C11#243511yescharacteristic
582C2×C11#243712yes—
583C2×C11#243712yes—
584C2×C11#247212yes—
585C2×C11#247212yes—
586C2×C11#256111yescharacteristic
587C2×C11#262611yescharacteristic
588C2×C11#284811yescharacteristic
589C24—22no—
590C24—22no—
591C24—22no—
592C24—22no—
593C24—28no—
594C24—28no—
595C24—216no—
596C24—28no—
597C24—216no—
598C24—22no—
599C24—22no—
600C24—22no—
601C24—22no—
602C24—22no—
603C24—22no—
604C24—22no—
605C24—22no—
606C24—22no—
607C24—22no—
608C24—22no—
609C24—22no—
610C24—28no—
611C24—28no—
612C24—48no—
613C24—48no—
614C24—48no—
615C24—48no—
616C24—48no—
617C24—48no—
618C24—48no—
619C24—48no—
620C24—48no—
621C24—44no—
622C24—44no—
623C24—48no—
624C24—44no—
625C24—44no—
626C24—44no—
627C24—44no—
628C24C2×Dic2214yes—
629C24C2×Dic2212yes—
630C24#433912yes—
631C24D4×D1114yes—
632C24D4×D1112yes—
633C24D4×D1112yes—
634C24#434114yes—
635C24#434112yes—
636C24#434112yes—
637C24C2×C22⋊D1112yes—
638C24C23×D1111yescharacteristic
639C2×Q8—228no—
640C2×Q8—448no—
641C2×Q8—444no—
642C2×Q8—448no—
643C2×Q8—444no—
644C22×C4—22no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—114no—
660C22×C4—112no—
661C22×C4—114no—
662C22×C4—112no—
663C22×C4—112no—
664C22×C4—112no—
665C22×C4—228no—
666C22×C4—221no—
667C22×C4—222no—
668C22×C4—221no—
669C22×C4—228no—
670C22×C4—228no—
671C22×C4—222no—
672C22×C4—222no—
673C22×C4—222no—
674C22×C4—222no—
675C22×C4—222no—
676C22×C4—221no—
677C22×C4—221no—
678C22×C4—221no—
679C22×C4—222no—
680C22×C4—222no—
681C22×C4—222no—
682C22×C4—222no—
683C22×C4—222no—
684C22×C4—222no—
685C22×C4—222no—
686C22×C4—221no—
687C22×C4—221no—
688C22×C4—221no—
689C22×C4—222no—
690C22×C4—222no—
691C22×C4—222no—
692C22×C4—222no—
693C22×C4—222no—
694C22×C4—222no—
695C22×C4—222no—
696C22×C4—444no—
697C22×C4—448no—
698C22×C4—448no—
699C22×C4—448no—
700C22×C4—448no—
701C22×C4—444no—
702C22×C4—444no—
703C22×C4C2×C22⋊D1112yes—
704C22×C4C2×C22⋊D1112yes—
705C4⋊C4—228no—
706C4⋊C4—228no—
707C4⋊C4—228no—
708C22⋊C4—28no—
709C22⋊C4—48no—
710C22⋊C4—48no—
711C22⋊C4—44no—
712C22⋊C4—2216no—
713C22⋊C4—2216no—
714C22⋊C4—228no—
715C22⋊C4—448no—
716C22⋊C4—448no—
717C22⋊C4—444no—
718C11#1471711yescharacteristic, complemented, Sylow
719C23—24no—
720C23—24no—
721C23—24no—
722C23—24no—
723C23—24no—
724C23—24no—
725C23—22no—
726C23—24no—
727C23—24no—
728C23—22no—
729C23—22no—
730C23—24no—
731C23—24no—
732C23—24no—
733C23—22no—
734C23—24no—
735C23—232no—
736C23—24no—
737C23—24no—
738C23—24no—
739C23—24no—
740C23—24no—
741C23—24no—
742C23—24no—
743C23—24no—
744C23—24no—
745C23—24no—
746C23—24no—
747C23—24no—
748C23—24no—
749C23—24no—
750C23—24no—
751C23—24no—
752C23—24no—
753C23—24no—
754C23—432no—
755C23—432no—
756C23—416no—
757C23—416no—
758C23—432no—
759C23—432no—
760C23—416no—
761C23—416no—
762C23—416no—
763C23—42no—
764C23—42no—
765C23—42no—
766C23—42no—
767C23—416no—
768C23—42no—
769C23—42no—
770C23—42no—
771C23—42no—
772C23—42no—
773C23—42no—
774C23—42no—
775C23—42no—
776C23—42no—
777C23—42no—
778C23—42no—
779C23—42no—
780C23#6693114yes—
781C23#6693114yes—
782C23#6693118yescomplemented
783C23#6693814yes—
784C23#6693814yes—
785C23#6697714yes—
786C23#6698914yes—
787C23#6699014yes—
788C23C22×Dic2211yescharacteristic
789C23C2×#433911yescharacteristic
790C23C2×D4×D1112yes—
791C23C2×D4×D1111yescharacteristic
792C23C2×D4×D1111yescharacteristic
793C23C2×#434111yescharacteristic
794C23C2×#434111yescharacteristic
795C23C2×#434112yes—
796C23#6703712yes—
797C23#6703712yes—
798C23C22×C22⋊D1111yescharacteristic
799Q8—4416no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—24no—
803C2×C4—24no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—41no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—114no—
818C2×C4—222no—
819C2×C4—224no—
820C2×C4—222no—
821C2×C4—224no—
822C2×C4—224no—
823C2×C4—222no—
824C2×C4—222no—
825C2×C4—222no—
826C2×C4—222no—
827C2×C4—224no—
828C2×C4—222no—
829C2×C4—224no—
830C2×C4—224no—
831C2×C4—224no—
832C2×C4—4416no—
833C2×C4—4416no—
834C2×C4—442no—
835C2×C4—442no—
836C2×C4—442no—
837C2×C4—442no—
838C2×C4—442no—
839C2×C4—441no—
840C2×C4—441no—
841C2×C4—441no—
842C2×C4—442no—
843C2×C4—442no—
844C2×C4—442no—
845C2×C4—441no—
846C2×C4—442no—
847C2×C4—442no—
848C2×C4—442no—
849C2×C4—442no—
850C2×C4—442no—
851C2×C4—442no—
852C2×C4—442no—
853C22—24no—
854C22—24no—
855C22—28no—
856C22—28no—
857C22—24no—
858C22—24no—
859C22—28no—
860C22—28no—
861C22—24no—
862C22—24no—
863C22—28no—
864C22—28no—
865C22—28no—
866C22—464no—
867C22—44no—
868C22—44no—
869C22—44no—
870C22—44no—
871C22—44no—
872C22—44no—
873C22—44no—
874C22—44no—
875C22—44no—
876C22—44no—
877C22—44no—
878C22—44no—
879C22#1062256018yescomplemented
880C22C2×#6693112yes—
881C22C2×#6693111yescharacteristic
882C22C2×#6693111yescharacteristic
883C22#1062301412yes—
884C22#1062302112yes—
885C22C2×#6693811yescharacteristic
886C22C2×#6693811yescharacteristic
887C22#1062302612yes—
888C22#1062311711yescharacteristic
889C22#1062311712yes—
890C22#1062311812yes—
891C22D11×#12011yescharacteristic
892C22#1062312011yescharacteristic
893C22#1062312112yes—
894C22#1062312212yes—
895C22#1062312212yes—
896C22#1062312311yescharacteristic
897C22#1062312412yes—
898C22C2×#6697711yescharacteristic
899C22C2×#6698911yescharacteristic
900C22C2×#6699011yescharacteristic
901C22D4×C22⋊D1112yes—
902C22#1062333712yes—
903C4—42no—
904C4—42no—
905C4—82no—
906C4—224no—
907C4—442no—
908C4—442no—
909C4—442no—
910C4—444no—
911C4—882no—
912C2—28no—
913C2—48no—
914C2C2×#1062256011yescharacteristic
915C2#1307192711yescharacteristic
916C2#1307193211yescharacteristic
917C2#1307226511yescharacteristic
918C2#1307227712yes—
919C2#1307228212yes—
920C2#1307273912yes—
921C2#1307274112yes—
922C2#1307377111yescharacteristic
923C2#1307442511yescharacteristic
924C2#1307690111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutator, socle, cosocleC24×C11C24
FittingC2×C11×#379C2
prime radicalC26×C11C22
hypercenterC2×#379D11
hypocenterC11#14717
LCSG ▷ C24×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#379

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×#66931C2semidirect
3. C2×#10622560C2semidirect
5. #13066861C2semidirect
6. #13066859C2semidirect
7. #13066859C2semidirect
8. #13066838C2semidirect
9. #13066838C2semidirect
10. #13066838C2semidirect
15. C23×Dic22C22semidirect
28. C22×C4⋊Dic11C22semidirect
29. C22×Dic11⋊C4C22semidirect
30. C22×Dic11⋊C4C22semidirect
36. C2×C11⋊#95C22semidirect
37. C2×C11⋊#95C22semidirect
38. C2×C11⋊#95C22semidirect
39. C2×C11⋊#95C22semidirect
40. C2×C11⋊#95C22semidirect
41. C2×C11⋊#95C22semidirect
53. C25×C11Q8semidirect
333. C23×C11C22⋊Q8semidirect
459. C22×C11#393semidirect
502. C25Dic22semidirect
718. C11#14717semidirect
782. C23#66931semidirect
879. C22#10622560semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×#669312
C23×C22⋊Dic112
C2×#106225602
C2×#106228602
#130668612
#130668592
#130668382
C2×C11×#3792
#1471711